#### Volume 1, issue 1 (1997)

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$\mathrm{Spin}^c$–structures and homotopy equivalences

### Robert E Gompf

Geometry & Topology 1 (1997) 41–50
 arXiv: math.GT/9705218
##### Abstract

We show that a homotopy equivalence between manifolds induces a correspondence between their spin${}^{c}$–structures, even in the presence of 2–torsion. This is proved by generalizing spin${}^{c}$–structures to Poincaré complexes. A procedure is given for explicitly computing the correspondence under reasonable hypotheses.

##### Keywords
4–manifold, Seiberg–Witten invariant, Poincaré complex
##### Mathematical Subject Classification
Primary: 57N13, 57R15
Secondary: 57P10, 57R19